A coin is flipped a total of 500 times in 10 batches of 50 f

A coin is flipped a total of 500 times, in 10 batches of 50 flips each. The number of heads in each of the batches is as follows 25, 27, 22, 24, 25, 24, 22, 26, 23, 26. Find the 95% confidence interval for the probability of heads assuming the method of batch means.

Solution

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=24.4
Standard deviation( sd )=1.7127
Sample Size(n)=10
Confidence Interval = [ 24.4 ± t a/2 ( 1.7127/ Sqrt ( 10) ) ]
= [ 24.4 - 2.262 * (0.542) , 24.4 + 2.262 * (0.542) ]
= [ 23.175,25.625 ]